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# Methods

## 1. Generation
Structures come from **CrystaLLM** (a language model trained on CIF files), prompted with a composition. Most
prompts are picked automatically ("autopilot"); a few were typed by a person. `origin` and `prompt` record which.

How the autopilot picks prompts changed on 2026-11-01 (`prompt_mode` records it from then on):
- before: 30% no composition (CrystaLLM chooses), 70% random cations and counts plus a random anion, with no
  charge balance. On our own hull data these random formulas were the worst source by far.
- since: 45% **substitution** (one element of a stable Alexandria compound swapped for a likely replacement:
  pymatgen's data-mined substitution probabilities for ions, same-group neighbours otherwise, metal-for-metal in
  intermetallics; formulas already in the 2.8M-structure training index removed; f-block lanthanides left out
  because plain PBE handles them poorly), 40% CrystaLLM chooses, 15% random but charge-balanced.

## 2. ML screen
Each structure is relaxed with **MACE** (float64). The verdict comes from the formation energy relative to the
elements and from how much the cell changed in relaxation:
`rock solid` / `plausible` / `borderline` / `unstable` / `falls apart`.

## 3. Novelty
Composition and structure are matched (pymatgen StructureMatcher) against a local index of known structures and,
since 2026-10-28, live against **Materials Project** and **Alexandria** via OPTIMADE. `known` and `rediscovered`
records include the matching ID. Before 2026-10-28 only the local index was used, which missed some known
compounds; affected records were re-audited.

Since 2026-11-03 a discovery must also be a **composition nobody has reported, in any structure**:
- before generation, autopilot formulas (substitution and random modes) are skipped if they appear in a local
  list of known compositions (the 2024 index above + current Alexandria PBE/PBEsol + both GNoME releases +
  Materials Project, rebuilt weekly); "surprise" crystals, where CrystaLLM picks the formula, are checked right
  after generation and skipped before MACE. The README's prompt-mode table counts these skips.
- before cataloguing, viable crystals get the online prior-art check described in §7 (about 32 sources incl.
  OQMD, COD, MPDS, NOMAD, OpenAlex and arXiv). A hit gives novelty `known composition` and no catalogue entry.
- a new arrangement of a known formula (the old `new structure` status) is no longer catalogued; the 638
  existing ones and every other catalogued record that failed the composition check were re-labelled
  `known composition` on 2026-11-03, with their old catalogue number and name kept in the novelty record.
- `control` prompts (5% of autopilot) ask for known stable compounds on purpose, to check that the generator and
  MACE still recognise real crystals. They are never catalogued.

## 4. ML convex hull
Nightly, catalogued structures get an energy above the hull: MACE energies of the candidate vs MACE-relaxed
Alexandria phases near the hull in the same chemical system. `decomposes_to` lists the hull products and
fractions. Values below about -0.15 eV/atom are flagged `suspect` (almost always an ML artefact).

## 5. DFT re-check
Candidates with ML e_hull ≤ 0.025 eV/atom and ≤ 30 atoms go to DFT, together with their decomposition products
on **Alexandria's PBE hull** (≤ 64 atoms each).

- Code: Quantum ESPRESSO 6.7, PBE, SSSP 1.1.2 efficiency pseudopotentials; cutoffs = max over the elements of the
  SSSP-recommended wavefunction/charge cutoffs.
- Smearing: Marzari-Vanderbilt, 0.01 Ry. Spin: non-magnetic, except systems containing Fe/Co/Ni/Mn/Cr, which
  are run spin-polarised from a 2 μB start on those atoms.
- Each structure: `vc-relax` on a coarse k-grid (spacing 0.4 Å⁻¹; forces 1e-3 Ry/bohr, pressure 0.5 kbar),
  then an `scf` on a finer grid (0.25 Å⁻¹, conv_thr 1e-7). Energies come from the final scf only.
- Candidate and competitors are computed with identical settings, so the hull is internally consistent.
- **Pass**: e_hull ≤ 0.025 eV/atom. That margin is about the size of PBE's typical error and of entropy at room
  temperature; a pass means "worth a closer look", nothing more.
- Some jobs carry a `note` (e.g. a relaxation stopped by hand when it was clearly not going to pass, or an
  extra competitor checked afterwards). Read it before using the number.

## 6. Properties (passes only)
PBE band gap and density of states at the Fermi level; elastic tensor from ±1% strains in the six Voigt directions (ions relaxed at
fixed cell), with Born stability check. PBE underestimates band gaps, often by a factor of ~2.

## 7. Phonons (passes only)
Since 2026-11-03 a pass first gets a composition check (`dft/<id>/novelty.json`, summarised in the
`prior_reports` column of `dft_results.csv`): any entry with the same reduced formula, in any structure, in
Materials Project, Alexandria, OQMD or COD, or the formula (every element ordering) in a paper title/abstract
indexed by OpenAlex. Any hit means no phonon run unless reviewed. This is wider than the structure match in §3:
#1856 SrCaCdP2 passed §3 but its structure is OQMD entry 5879242 (a computed prediction, no ICSD record).

phonopy finite displacements on a supercell with every side ≥ 7 Å, after a tight fixed-cell relaxation;
frequencies on a 10×10×10 mesh. Any mode softer than -0.1 THz away from the Γ acoustic modes = unstable. The
supercell is small, so long-wavelength instabilities can be missed.

## Known limits
- Hulls only include competitors that exist in Alexandria (and, for the ML hull, phases near its hull). A missing
  competitor can make a candidate look more stable than it is.
- PBE alone; no van der Waals, no Hubbard U, no finite-temperature free energies.
- Pass ≠ synthesisable. No candidate here has been made in a lab.